Research has shown that apparent (psychological) scaling may not be the total answer because they are often based on the “average” map reader.

Range grading proportional symbols may be a better choice.In this scaling method, each symbol represents a range of data values rather than individual values.

In other words, symbol-size discrimination is the design goal rather than magnitude estimation.Range Grading Scaling

Create a long skinny rectangle (always use the same width).

Adjust the height to fit your calculations, comparing it with your values.

Move it to the desired location.

Duplicate the first symbol as often as needed and vary the height for each symbol in turn. Remember the columns should all have the SAME WIDTH. Only the height varies.How to Calculate your Linear Symbol Size

Symbol Size = (max symbol size) x (value /max value)How to Calculate Your Linear Symbol SizeDraw the symbol for the shape that you chose. It doesn't matter if you use this size as the diameter of a circle, the side of a square, the side of a triangle, or the height of a picture of a leaf or a house. They will all be in the proper proportion.

Select a circle from the drawing tool menu. Adjust it’s size to make it fit your calculations (about 0.64 cm across in this example), and move it to the correct place on the map.How To Draw Symbols on Your Map

1. Make a list of the values2. Find the square roots of those values. 3. Then work from the square roots list instead of the original list. 4. Choose a maximum symbol size (For example, a circle with 2 cm diameter). The largest symbol represents the largest value.How to Calculate Your Symbol SizeThe difference between the two methods can be seen in the two maps below.Absolute vs Perceptual ScalingTwo types of data can be mapped by proportional symbols:True point data: Data occur at points, e.g. yields of oil wells, symbol can be placed at the exact location;

Conceptual point data: Data are collected over an area, but conceived as being aggregated and located at points within the area; e.g. oil yields of counties.

Symbols are placed at the centroid points of areal units.

Any magnitude such as totals, ratios, and proportion can be mapped with proportional symbol maps, but density is normally symbolized by the choropleth technique instead of proportional symbol technique.Proportional Symbol MapsPoint symbol can be segmented, colored, sectored

As you can see here the size and color of the symbol has been changed.

A good design approach is to limit the number of variables symbolized by proportional point symbols to one or two but never three or moreOverloaded Proportional Point SymbolsStack symbols on top of one another

Enhance figure-ground contrast because the proportional symbols tend to appear as a figure against the background of the rest of the map.

Also promotes a visual hierarchy, as the circles appear “above” other map information (such as a road network).Enable map readers to see through overlapping symbols

Allow background information to be seen beneath the symbols.Symbol OverlapLarge symbols result in large overlap

The fill within symbols can be varied from white to solid black. Black-filled circles are judged best, as well as gray-filled symbols.

Different colors can be used for the boundary and interior of symbols.Handling Symbol OverlapLinear vertical arrangement

Order based on available map space. Linear Legend DesignLinear Legend DesignSymbols are placed adjacent to each other in either a horizontal or vertical orientation.

Permits a solid fill and tend to enhance figure-ground contrast.

For a linear horizontal arrangement, the symbols should be ordered with the smallest on the left and the largest on right if the map space is available.Proportional Symbol Legend DesignColumns - the bases inside the regions represented by the data.

The HEIGHT of each column is proportional to the value.Column MapCreate three or four extra symbols for round numbers near the bottom, middle and top of your range of values for a legend. For example, if the original values range from 122,500 to 20,250,000 (giving square roots ranging from 350 to 4500), you might use values of 200,000, 5,000,000 and 20,000,000 in your legend.

Remember to use the square roots to calculate symbol sizes for the legend, but label them with the ORIGINAL values!Square root scaling for two-dimensional symbols:

Each value in the data set is represented by an absolutely scaled symbol.

Different values correspond to symbols of different sizes.

Proportional symbol maps are often constructed by beginning with a largest symbol size to minimize the effect of symbol overlap.

Methods for Scaling Point SymbolSpheres, cubes, prisms

Greater data ranges can be handled on the map if three-dimensional geometric symbols are used. Less crowding of symbols.

Very pleasing and eye-catching graphics. Most map-readers have a difficulty to gauge their scaled values correctly.

Increasingly greater ease of construction because of computer-based mappingPictograph SymbolProportional point symbol mapping requires compact geometric symbols at points, and the circle is one of the most popular symbols.Two-dimensional Geometric symbolCircles, squares, triangles, etc.Area is the geometric characteristic that is customarily scaled to geographical magnitudes.

Circles have been most frequently used because they are visually stable and conserve map space.Point SymbolsProportional Symbol MappingUse an exponent of 0.57 instead of 0.5 in the circle scaling formula.Flannery correction:Psychological investigations show that most people do not (or cannot) respond to the geometric properties of quantitative symbols in a linear fashion. People tend to underestimate the size of larger symbols

A correction factor, known as the Flannery correction factor, is used to make the symbol (circle) appear larger as their values increase to compensate for the underestimation of larger symbols in relation to smaller ones.Methods for Scaling Point SymbolCalculating Area Symbols and Drawing them on Your MapProportional Symbol MapsRange Grading/Legend DesignSymbol OverlapAbsolute/Mathematical Scaling(Square root method)Perceptual ScalingSymbol Size FormulaLinear Symbol Size FormulaColumn MapsTransparent SymbolsOpaque SymbolsTutorialAudio ClipsMost slides in this presentation include audio clips of the lecture material. If you place your mouse at the bottom of the screen you will see the playback controls. Press play and pause to hear/stop the audio.SlidesTo progress to the next slide, click the right arrow found at the bottom-center of your screenAs the audio plays, you can pan and zoom around the presentation. The audio will only end if:you press the pause buttonyou go to the next slideor it runs to the endTutorialAudio ClipsMost slides in this presentation include audio clips of the lecture material. If you place your mouse at the bottom of the screen you will see the playback controls. Press play and pause to hear/stop the audio.SlidesTo progress to the next slide, click the right arrow found at the bottom-center of your screenAs the audio plays, you can pan and zoom around the presentation. The audio will only end if:you press the pause buttonyou go to the next slideor it runs to the end